1. Field of the Invention
The present invention relates to oil and gas reservoir simulation and more particularly related to a machine, computer program product, and method to enable scalable parallel processing of oil and gas reservoirs for a variety of simulation model sizes.
2. Description of Prior Art
A subterranean geologic body or formation contains multi-phase, multi-component fluids, and accordingly a petroleum reservoir may contain oil, natural gas, water and several constituent compounds, that may be modeled to predict the fluid flow from a reservoir, which is also known as reservoir simulation. Reservoir simulation models may be run before or after a well is drilled to determine production rate, etc. for the various methods.
Current reservoir modeling techniques create a numerical grid of the reservoir comprised of a plurality of grid cells, and process data in the finite volume of each grid cell. Because reservoirs can be very large and complex, and grid cells can number in the millions to over one billion, the simulation models can take several hours to days to run. The desirable runtime is in the minutes to a few hours maximum as hundreds of runs are usually required for history matching. Accordingly, Saudi Aramco's POWERS™ program was created to speed up data processing using parallel computing. Parallel computing, as performed by the POWERS™ program, divides the numerical grid into a plurality of domains, with each domain consisting of a plurality of grid cells. The numerical grid is a structured grid, meaning each grid cell can be described the same, i.e., each inner vertex is incident to a fixed number of cells and each cell is defined by a fixed number of faces and edges. Structured grids may use Cartesian coordinate (I, J, K), or some other similar mapping method to locate grid cells for data processing. To run the simulations, rock properties, described using geologic models (porosity, permeability, etc.) as well as the geometry of the rock formation and data related to the well bore, are read into each computer. Because the domain is sub-divided into several finite volumes, or grid cells, conservation equations of mass, momentum, and energy are then constructed for each grid cell. These balance equations represent the discrete time rate of change of these quantities stored in the grid block due to the inter-block fluxes and sources and sinks of the quantities due to the physical and chemical processes being modeled, and are accordingly a set of discrete non-linear partial differential equations involving complex functions. Finally, using the mapping method for the grid, each computer can arrange for cross talk with other computers to simulate flow through the domains. FIG. 1 shows a prior art, two-dimensional structured grid of a reservoir with a multi-lateral well disposed therein. As can be seen, each grid cell is uniform, regardless of the geological feature or proximity of the grid cell to the well.
Unfortunately, reservoirs are of a sedimentary origin and have multiple layers that have thicknesses and depth variations throughout, which do not neatly follow the pattern of a structured grid. For example, a layer can disappear locally due to lack of deposition or subsequent erosion, which is known as a pinch-out. Also, uplifting (the raising of the earth's crust) and subsidence (the lowering of the earth's crust) over geologic time can lead to faulting and fracturing of the layers. In addition to the complexity of the reservoir layers, complex wells may be drilled into the reservoirs to extracts fluids from them or to inject fluids into them for pressure maintenance or enhance-oil-recovery operations, i.e., these wells may be multi-branched. Simply a structured grid does not produce accurate flow models in these circumstances. Better, unstructured grids, built to represent the geologic layers and well would represent faults, fractures, pinch-outs and well geometry, are required for accuracy.
To create unstructured grids, oil or gas reservoirs are subdivided into non-uniform elementary finite-volumes, i.e., grid cells or grid blocks. These grid cells can have variable numbers of faces and edges that are positioned to honor physical boundaries of geological structures and well geometry embedded within the reservoir. Accordingly, these maps may be very complex. Examples of unstructured gridding methods includes Voronoi diagrams, i.e., a grid where each cell has faces and edges that are closer to one Voronoi site or point than any other Voronoi site or point. FIG. 2 is an example of a two dimensional Voronoi grid. While unstructured grids more accurately reflect the geological features of the geological body, in order to perform unstructured grid simulation using parallel processing techniques, the global coordinate system, e.g., (I,J,K) Cartesian indexing, must be replaced with a global hash table, accessible by the computer processing each domain, to arrange for cell and domain cross-talk. Unfortunately, the global hash table for a model with, e.g., tens of millions to over a billion cells, can overwhelm the memory of for each of the parallel computers.
In addition to the problems with prior art reservoir grids, simulating reservoirs having multi-lateral wells require more data input and use more complex algorithms, and simulation models for this types of production methods can be very cumbersome—even using the POWERS™ system. The computational complexity of these equations is further complicated by geological model size is typically in the tens of millions to hundreds of millions of grid cells. Since finding a solution to several million to a few billion nonlinear partial differential equations with multiphase discontinuities is computationally expensive, reservoir simulation models are usually built at a coarser scale than the geologic model via a process known as upscaling, i.e., the averaging of rock properties for a plurality of grid cells. While computationally more efficient, upscaling renders the simulation model inaccurate. It is very desirable to develop simulation system that can directly use the original geologic model without upscaling and can honor complex well geometries and geology at the same time.
Therefore, the machine, methods, and program products in this invention constitute the enabling technology to do scalable parallel reservoir simulation of a desired model sizes (from small models to over one-billion-cell models) using both unstructured grids for complex reservoirs and multi-lateral wells, and structured grids at seismic-scale geologic model without upscaling.